Solution
| Teams | Played | Wins | Losses | Draws | Points |
|---|---|---|---|---|---|
| A | 5 | 3 | 0 | 2 | 8 |
| B | 5 | 3 | 2 | 0 | 6 |
| C | 5 | 2 | 2 | 1 | 5 |
| D | 5 | 1 | 1 | 3 | 5 |
| E | 5 | 1 | |||
| F | 5 |
From the given points, we can figure out from A to D how their matches went, i.e. how many they won, lost, or ended with a draw.
| Teams | Played | Wins | Losses | Draws | Points |
|---|---|---|---|---|---|
| A | 5 | 3 | 0 | 2 | 8 |
| B | 5 | 3 | 2 | 0 | 6 |
| C | 5 | 2 | 2 | 1 | 5 |
| D | 5 | 1 | 1 | 3 | 5 |
| E | 5 | 0 | 1 | 4 | 4 |
| F | 5 |
We know that E and F have less than 5 points each. It's given that E has one loss, so now he has 4 more matches. All 4 of these have to be draws, because that's the only case where E will have less than 5 points. Even a single win would exceed the points and contradict what's given.
| Teams | Played | Wins | Losses | Draws | Points |
|---|---|---|---|---|---|
| A | 5 | 3 | 0 | 2 | 8 |
| B | 5 | 3 | 2 | 0 | 6 |
| C | 5 | 2 | 2 | 1 | 5 |
| D | 5 | 1 | 1 | 3 | 5 |
| E | 5 | 0 | 1 | 4 | 4 |
| F | 5 | 0 | 3 | 2 | 2 |
Things to note:
Total Number of Points , since there will be a total of matches and each match results in two points (if a team loses, the winning team gets two points and if a match ends in a draw, both teams get one point each)
Hence, points
points
F could have either 1 win, 4 losses, 0 draws or 0 wins, 3 losses, and 2 draws.
The table becomes inconsistent with the former, since no two teams can have 0 draws and B already has 0 draws.
Hence, the table above is our table.
From it, we can see that D has suffered one loss only, and it is given that C defeated D. Hence, D was not defeated by A.
More from this set:
Question 16
Question 17
Question 18
Question 20